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Transcript of 3rdpipes and Cisterns New1
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 1
SREENIVASA INSTITUTE OF TECHNOLOGY AND
MANAGEMENT STUDIES
Murukambattu Post, Chittoor – 517 127 (A.P)
AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY –
ANANTAPUR,
Course material
For
Reasoning and Quantitative Aptitude
Module Name: PIPES AND CISTERNS
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 2
PREREQUISITES:
1. Inlet:
A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as aninlet.
Outlet:
A pipe connected with a tank or cistern or reservoir, emptying it, is known as anoutlet.
2. If a pipe can fill a tank in x hours, then:
part filled in 1 hour =1.
x
3. If a pipe can empty a tank in y hours, then:
part emptied in 1 hour =1.
y
4. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours(where y > x), then on opening both the pipes, then
the net part filled in 1 hour =1-1
.x y
5. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours(where y > x), then on opening both the pipes, then
the net part emptied in 1 hour = 1-1 .
6.Time for filling , (Filling pipe is bigger in size.)
F = (e * f)/(e - f)
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 3
7.Time for emptying , (emptying pipe is bigger in size.)
E = (f * e)/(f - e)
8.Pipes 'A' & 'B' can fill a tank in f1hrs & f2hrs respectively.Another pipe 'C' can empty thefull tank in 'e'hrs.If the three pipes are opened simultaneously then the tank is filled in
F = L/[(L/f1) + (L/f2) - (L/e)]
9.Two taps 'A' & 'B' can fill a tank in 't1' & 't2' hrs respectively.Another pipe 'C' can empty thefull tank in 'e'hrs.If the tank is full & all the three pipes are opened simultaneously . Then thetank will be emptied in,
E = L/[(L/e) - (L/f1) - (L/f2)]
10.A filling tap can fill a tank in 'f'hrs.But it takes 'e'hrs longer due to a leak at the bottom.Theleak will empty the full tank in ,
E = [t(f * e) * tf]/[t(f + e) - tf]
11.Capacity of the tank is ,
F = (f * e)/(e - f)
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 4
Solved Examples
1. Two taps A and B can fill a tank in 10 hours and 15 hours and 15 hours
respectively. If both the taps are opened together, the tank will be full in ?
Ans:6hrs
Basic Formula:
If A can do a piece of work in x hours and B can do a piece of work in y hours. Then
A and B together will do the work inyx
xy
hours
Answer with Explanation:
Time taken by A = 10 hours
Time taken by B = 15 hours
Time taken by A and B =1015
1015
X
=25
1015X= 6 hours.
2. To fill a cistern, pipes A, B and C take 20 minutes, 15 minute and 12 minutes
respectively. The time in minutes that the three pipes together will take to fill the cistern is:
Ans:5 TCS 2008
Basic Formula:
A can do a piece of work in x minutes
B can do a piece of work in y minutes
C can do a piece of work in z minutes
Minute’s work of each of the three is 1/x +1/y + 1/z
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 5
Answer with Explanation:
1 minutes work of each of the three pipes
= 1/20 + 1/15 + 1/12
=60
543 =
60
12
= 1/5
= 5 minutes
3. Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties the
full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank
will be filled?
Ans;7 hrs 30 mins
Basic Formula:
Pipe A can fill a tank in x hours and pipe B can fill a tank in y hours and pipe C can empty it
in z hours. If all the pipes are operate simultaneously,
1 hours of work of each of the three pipes = 1/x +1/y - 1/z
Answer with Explanation:
1 minutes work of each of the three pipes
= 1/10 + 1/12 - 1/20
=60
356 =
60
8
=15
2
= 15/2 hours = 7 ½ hour
= 7 hours 30 minutes.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 6
4. A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If
the cistern is full, then the time that the leak will take to empty it is: CAT 2007
Ans:90 hrs
Basic Formula:
If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be
filled (empty) inyx
xy
hours
Answer with Explanation:
Time taken by A = 9 hours
Time taken by B = 10 hours
Time taken by A and B =910
109
x
= 90 hours.
5. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 ½
hours to fill the tank. The leak can drain out of all the water of the tank in:
Ans:21 hrs
Basic Formula:
If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled
(empty) inyx
xy
hours
Answer with Explanation:
Time taken = 3 hours
Time taken = 3 ½ hours
Time taken by A and B =3
2
13
2
133
x
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 7
=3
2
72
73
x
=
2
672
73
x
= 21 hours
6. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both
are opened and A is closed after 3 minutes. How much further time would it take for B to fill
the bucket? WIPRO 2009
Ans 8 min 15 sec
Basic Formula:
Total work (to fill or empty) = I part + II part =1
Find I st part and subtract it from ‘1’ , then multiply the required section value to find
the answer.
Answer with Explanation:
For 3 minutes (I part)
= 3
15
1
12
1
= 3
1215
1215
X
= 3
20
3= 9/20
Remaining part
= 1- 9/20 = 11/20
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 8
Tap B fill the bucket in
=20
11-15
= 33/4 = 8 ¼ hours
= 8 hours 15 seconds.
7. A tank can be filled by a tap in 20 minutes and by another tap in 60 mintues. Both
taps are kept open for 10 mintues and then the first tap is shut off. After this, the tank will be
completely filled in:
Ans:20 min
Basic Formula:
Total work (to fill or empty) = I part + II part =1
Answer with Explanation:
For 10 minutes (I part)
= 10
60
1
20
1
= 10
60
4
= 4/6 = 2/3
Remaining part
= 1- ( I part)
= 1-2/3
= 1/3
The tank will be complete by filled in (B only, after 10 minutes)
= 1/3 X 60
= 20 minutes.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 9
8. If two pipes function simultaneously the reservoir will be filled in 12 hours, one
pipe fills the reservoir 10 hours faster than the other. How many hours it takes the second
pipe to fill the reservoir? ACCENTURE 2008
Ans:30 hours
Basic Formula:
Taken unknown value as x and useyx
xy
Answer with Explanation:
Let the reservoir be filled by forst pipe in x hours, therefore the second pipe will fill it in
(x+10) hours.
1/x + 1/ x+10 = 1/12
)10(
10
xx
xx= 1/12
12 (10+2x) = x2 +10x
x2 +10x – 24x – 120 = 0
x2 – 14x – 120 = 0
(x-20) (x+6) = 0
x = 20 (x should nor –ve)
The second pipe can take (x+10) = 20 + 10 = 30 hours, to fill the reservoir.
One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. How
long will they take to fill the cistern if both the taps are opened?
Ans: 6hours
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 10
Basic Formula:
Pipe A can fill a tank in ‘x’ hours and pipe B can empty it in ‘y’ hours. If both the pipes
opened together, the tank will be filled inyx
xy
hours.
Answer with Explanation:
Time taken to fill the tank = 2 hours
Time taken to empty the tank = 3 hours
Time taken to fill the cistern =13
32
X
= 6 hours.
9. 12 buckets of water fill a taken when the capacity of each bucked is 13.5 liter. How
many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres ?
Ans:18 CTS 2007
Basic Formula:
Here the tank is same
Number of buckets X capacity of bucket = Number of buckets X capacity of bucket
Answer with Explanation:
The capacity of the tank is same,
N1 X W1 = N2X W2
N1 = No. of Buckets W1 = Capacity of liters in the buckets
N2 = No. of Buckets W2 = Capacity of liters in the buckets
= 12 X 13.5 = N2 X9
= N2 =9
5.1312X= 54/3
= N2 = 18
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 11
10. Bucket p has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the
empty drum. How many turns it will take for both the buckets p and q having each turn
together to fill the empty drum:
Answer:45
Basic Formula:
yx
xy
Answer with Explanation:
Bucket P has thrice the capacity as bucket Q
Q= 3 P
P takes 60 turns
Q takes = 180 turns
P and Q takes =18060
60180
X
=240
60180X
= 45 turns.
11. Two pipes A and B fill a tank in 15 hours and 20 hours respectively while a third
pipe c can empty the full tank in 25 hours. All the three pipes are opened in the beginning,
after 10 hours, c is closed. In how much time, will the tank be full ? ans:12 hrs
Basic Formula:
1/x +1/y - 1/z Part I and Part II = 1
Answer with Explanation:
A B C
15 20 -25
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 12
For 10 hours = 10
25
1
20
1
15
1
= 10
300
12
300
15
300
20
= 10
300
23
= 23/30 ( Part I)
Remaining part =1- 23/30 = 7/30
(A+B)’s 1 hour work
= 1/15 + 1/20 = 4/60 + 3/60
= 7/60
Therefore = 7/30 X 60/7 = 2 hours
Hence 10+2 = 12 hours
12. Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respectively
but a third pipe c can empty the full tank in 6 mintues. A and B are kept open for 5 minutes in
the beginning and then c is also opened. In what time is the cistern emptied …..
Ans:45 mints
Basic Formula:
1/x +1/y - 1/z
Answer with Explanation:
A B C
12 15 -6
For 5 minutes = 5
15
1
12
1
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 13
= 5
180
27
= ¾
When all the three pipes are opened = 1/12 + 1/15 – 1/6
= 15/180 + 12/180 – 30/180
= -3/180 = -1/60 (-means emptying)
Empty the cistern in 1 min is 1/60
Therefore ¾ will emptied in ¾ X 60 = 45 minutes.
13. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for
2hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours
taken by C alone to fill the cistern is: INFOSYS 2008
Answer:14
Basic Formula:
C’s work = (A+B+C)’s work – (A+B)’s work
Answer with Explanation:
A+B+C = 1/6
For 2 hours = 2 (1/6) = 1/3
Remaining = 2/3
(A+B)’s 7 hours work = 2/3
(A+B)’s 1 hours work = 2/21
C’s 1 hour work = (A+B+C)’s work – (A+B)’s work
= 1/6 -2/21
= 9/126 = 1/14
C alone can fill the tank in 14 hours
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 14
14. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills
water are the rate of 6 liters a minute. When the tank is full, the inlet is opened and due to the
leak, the tank is empty in 12 hours. How many litres does the cistern hold ?
Ans: 8,640
Basic Formula:
Work done = 1/x – 1/y
Time X number of liters
Answer with Explanation:
Time taken to fill the tank is 1/8
Time taken to empty the taken is 1/12
Work done by the inlet in 1 hour =
12
1
8
1=
812
812
X
=812
4
X= 1/24
Work done by the inlet in 1 minute = 1/24 X 1/60 = 1/1440
Therefore Volume = 1440 X6 liters
= 8640 liters
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 15
Solved problems
1.A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at
the rate of 4 litres a minute. When the tank is full the inlet is opened and due to the leak the
tank is empty in 8 hours. The capacity of the tank in litres is : Ans 5760. CAT 2010
Basic Formula:
Work done = 1/x – 1/y
Time X number of liters
Answer with Explanation:
Time taken to fill the tank is 1/6 hour (Time taken to empty = time taken to full)
Time taken to empty the tank is 1/8
Work done by the inlet in 1 hour = (1/6 – 1/8)
=86
68
X
= 2 / 48 = 1/24
For 1 minute = 1/24X1/60 = 1/1440
An inlet pipe fill water at the rate of 4 liters a minute = 1440 X 4 = 5760 liters
02.A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is
already half-full and both tanks are opened together, the tank will be :
Ans: emptied in 8 min
Basic Formula:
Work done = 1/x – 1/y
Answer with Explanation:
Time taken to fill the tank in = 1/16 min
Time taken to empty the tank in = 1/8 min
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 16
Work done by both in 1 min = (1/16 – 1/8)
=816
168
X
= -8 / 16X8
= -1/16 (-ve means empty)
Now full tank will be emptied by them in 16 min
Half tank will be emptied in 8 min.
03.A cistern has two taps which fill it in 12 min and 15 min respectively. There is also a
waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20
mintues. How long will waste pipe take to empty the full cistern ?
Ans;10 min
Basic Formula:
C’s work = (A+B+C)’s work – (A+B)’s work
A + B = 1/x+1/y
Answer with Explanation:
To fill the cistern = (1/12 + 1/15) =1512
27
X
= 3/20
Work done by waste pipe in 1 min
= work done by all the three taps – work done by two taps (fill)
= 1/20 – 3/20 = -2/20 = -1/10 (-ve means empty)
Waste pipe will empty the full cistern in 10 minutes.
04.Two pipes A and B can fill a cistern in 12 minutes and 15 mint respectively. If both the
pipes are opened together, then after how much time B should be closed so that the tank is
full in 9 minutes? CAT 2010
Ans 4 min
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 17
Basic Formula:
Let B be closed after x minutes.
I part + II part = 1
I part = Cistern filled by (A+B) in x min
II part = Cistern filled by A in (9-x) minutes
Answer with Explanation:
16
1
12
1x + (9-x) X 1/12 = 1
1212
9
1612
1216 x
Xx
= 1
x1612
28
x- x/12 = 1-9/12
12412
7 x
x
x = 3/12
7x – 4x = 12
3x = 12
X = 4
So, B must be closed after 4 minutes.
05. A water tank is two – fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty
it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank
completely?
Answer : 6 minutes
Basic Formula:
AB/B-A
Answer with Explanation:
Water level in the tank is 2/5
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 18
Both the pipes are open =610
610
X
=
60
4=
15
1
Therefore 2/5 X15 = 6 minutes
06.. Pipes A and B take 20 and 30 minutes to fill a tank respectively. The 2 together will take
Answer : 12
Basic Formula:
AB/A+ B
Answer with Explanation:
A = 20
B = 30
Together = A+B/AB
=3020
3020
X
=3020
50
X=
12
1
Therefore 12 minutes.
07.. 2 pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both are opened
simultaneously, how much time will be taken to fill the tank?
Answer : 20 hours
Basic Formula:
Time taken to fill the tank = A+B/AB
Answer with Explanation:
A = 36
B = 45
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 19
BA
AB
=
4536
4536
X
=81
4536X
= 20 hours
08.Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are
opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall
be full ? INFOSYS 2007
Ans: 5 hours
Basic Formula:
It’s an alternate hour’s problem
A’s 1hour work = 1/6
B’s 1 hour work = ¼
A + B means 2 hours of work
Answer with Explanation:
(A+B)’s 2 hours work when opened alternately =
4
1
6
1=
24
64
(A+B)’s 4 hours work when opened alternately = 2 (5/12) = 5/6
Remaining = 1-5/6 =1/6
It is A’s turn and 1/6 part is filled by A in 1 hour
Total time taken to fill the tank = (4+1) hours
= 5 hours
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 20
9.A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe
meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each
of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the
tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill
pipes?
(1) 2 (2) 4 (3) 6 (4) 5
Correct Answer - (2)
Solution:
Let the number of fill pipes be ‘n'. Therefore, there will be 8-n, waste pipes.Each of the fill pipes can fill the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8th
of the tank in an hour.Hence, n fill pipes will fill n/8th of the tank in an hour.
Similarly, each of the waste pipes will drain the full tank in 6 hours. That is, each of the wastepipes will drain 1/6th of the tank in an hour.Therefore, (8-n) waste pipes will drain ((8-n)/6)th of the tank in an hour.
Between the fill pipes and the waste pipes, they drain the tank in 6 hours. That is, when all 8of them are opened, 1/6th of the tank gets drained in an hour.
(Amount of water filled by fill pipes in 1 hour - Amount of water drained by waste pipes 1hour)= 1/6th capacity of the tank drained in 1 hour.
n/8 - 8-n / 6 = -1/6 => 6n-64+8n / 48 = -1/6 => 14n-64= -8 or 14n = 56 or n=4
Note: In problems pertaining to Pipes and Cisterns, as a general rule find out the amount ofthe tank that gets filled or drained by each of the pipes in unit time (say in 1 minute or 1hour).
10.There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others
are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes
can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an
empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
(1) 6 (2) 8 (3) 7 (4) 5
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 21
ANS:3
Solution
Let there be ‘n’ fill pipes attached to the tank.Therefore, there will be 12 - n drain pipes attached to the tank
Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8th of thetank in an hour.Hence, n fill pipes will fill n*1/8 = n/8 th of the tank in an hour.Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain1/6 th of the tank in an hour.Hence, 12 - n drain pipes will drain(12-n) / 6 = 12-n / of the tank in an hour.When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow.Therefore, in an hour 1/24 thof the tank gets filled.Hence,n/8 - 12 - n/6 = 1/24.i.e.3n - 4(12-n) / 24 = 1/24 or 7n - 48 = 1 => 7n = 49 or n = 7.
11.A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3.
The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is the
emptying capacity of the pump if the pump needs 12 more minutes to fill the tank than to
empty it?
(1) 50 m3 / min (2) 60 m3 / min (3) 45 m3 / min (4) 90 m3 /min
Correct Answer - (2)
Solution:
Let ‘f’ m3/min be the filling capacity of the pump. Therefore, the emptying capacity of the
pump will be= (f + 10) m3 / min.
The time taken to fill the tank will be = 3600 / f minutes
And the time taken to empty the tank will be = 3600 / f+10.
We know that it takes 12 more minutes to fill the tank than to empty it
i.e 3600/f - 3600 / f+10 = 12 => 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 22
=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.
Solving for positive value of ‘f’ we get, f = 50.
Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min
12.Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it
takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank
if pipe A is shut?
(1) 2 hours 30 minutes (2) 5 hours (3) 4 hours (4) 10 hours
Correct Answer - (4)
Solution:
Pipe A fills the tank normally in 2 hours. Therefore, it will fill ½ of the tank in an hour.
Let the leak take x hours to empty a full tank when pipe A is shut. Therefore, the leak will
empty 1/4 of the tank in an hour.
The net amount of water that gets filled in the tank in an hour when pipe A is open and when
there is a leak = 1/2 -1/x of the tank. — (1)
When there is a leak, the problem states that Pipe A takes two and a half hours to fill the tank.
i.e. 5/2 hours. Therefore, in an hour, 5/2 th of the tank gets filled. – (2)
Equating (1) and (2), we get 1/2 - 1/x =2/5=> 1/x = 1/2 - 2/5 = 1/10 => x = 10 hours.
13. There are 12 pipes attached to a tank. Some of them are fill pipes and some are drain
pipes. Each of the fill pipes can fill the tank in 12 hours, while each of the drain pipes will
take 24 hours to drain a full tank completely. If all the pipes are kept open when the tank was
empty, it takes 2 hours for the tank to overflow. How many of these pipes are drain pipes?
(1) 6 (2) 11 (3) 4 (4) 7
Correct Answer - (3)
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 23
There are 12 pipes attached to the tank. Let ‘n’ of them be fill pipes. Therefore, there will be
12-n drain pipes.
Each fill pipe, fills the tank in 12 hours. Therefore, 1/12th of the tank gets filled every hour
by one fill pipe.
‘n’ fill pipes will, therefore, fill n/12 th of the tank in an hour.
Each drain pipe drains the tank in 24 hours. That is, 1/24 th of the tank gets drained by one
drain pipe every hour.
12-n drain pipes, will therefore, drain 12-n / 24 th of the tank in an hour.
When all the pipes are open when the tank is empty, it takes 2 hours for the tank to overflow.
i.e. ½ the tank gets filled every hour.
Equating the information, we get n/12 - 12-n/24 = 1/2
=> 2n+n-12 / 24 = 1/2 => 3n - 12 = 12 or 3n = 24 or n = 8.
Therefore, there are 8 fill pipes and (12 - 8) = 4 drain pipes.
14.Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom of the tank it takes
thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a
full tank, when pipe A is kept closed? CAT 2010
(1) (3/2)a hours (2) (2/3)a (3) (4/3)a (4) (3/4)a
Correct Answer - (1)
Solution:
Pipe A fills the tank in 'a' hours. Therefore, of the tank gets filled in an hour. On account of
the leak it takes 3a hours to fill the tank. Therefore, of the tank gets filled in an hour. Let the
leak at the bottom of the tank take 'x' hours to empty the tank. Hence, 1/x of the tank gets
emptied every hour.
1/a - 1/x =1/3a => 1/x =1/a - 1/3a = 2/3a
Hence, x = 3a/2
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 24
15.Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. Ifboth the pipes were kept open when the tank is empty, how much time will it take for the tankto overflow?
Explanatory AnswerPipe B fills the tank 5 times as fast as pipe A.Therefore, pipe B will fill the tank in one-fifth of the time that pipe A takes.
Pipe B will fill the tank in = 6 minutes.
In 1 minute, pipe A will fill th of the tank and pipe B will fill th of the tank.
Therefore, together, the two pipes will fill th of the tank in a minuteHence, the two pipes working together will take 5 minutes to fill the tank.
16.Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and
10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C
discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R
in the liquid in the tank after 3 minutes?
A.5
11B.
6
11
C.7
11D.
8
11
Answer: Option B
Explanation:
Part filled by (A + B + C) in 3 minutes = 31
+1
+1
= 3 x11
=11
.30 20 10 60 20
.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 25
Part filled by C in 3 minutes = 3
10
Required ratio =3
x20
=6
.10 11 11
17. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C canempty it in 12 hours. If all the three pipes are opened together, then the tankwill be filled in:
A. 113
hours17
B.28
hours11
C. 39
hours17
D.41hours
2
Answer: Option C
Explanation:
Net part filled in 1 hour1+
1-
1=
17.
5 6 12 60
The tank will be full in60
hours i.e., 39
hours.17 17
18.A pump can fill a tank with water in 2 hours. Because of la leak, it took 2 hours to fillthe tank. The leak can drain all the water of the tank in:
A. 41hours
3B.7 hours
C. 8 hours D.14 hours
Answer: Option D
Explanation:
Work done by the leak in 1 hour =1-3
=1
.2 7 14
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 26
Leak will empty the tank in 14 hrs.
19.Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Bothpipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A.5 min. B.9 min.
C.10 min. D.15 min.
Answer: Option B
Explanation:
Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
x2
+1
+ (30 - x).2
= 175 45 75
11x+
(60 -2x)= 1
225 75
11x + 180 - 6x = 225.
x = 9.
20.A tank is filled by three pipes with uniform flow. The first two pipes operatingsimultaneously fill the tank in the same time during which the tank is filled by the third pipealone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower thanthe third pipe. The time required by the first pipe is:
A.6 hours B.10 hours
C.15 hours D.30 hours
Answer: Option C
Explanation:
Suppose, first pipe alone takes x hours to fill the tank .
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 27
Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
1+
1=
1
x (x - 5) (x - 9)
x - 5 + x=
1
x(x - 5) (x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
x = 15. [neglecting x = 3]
21.Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3gallons per minute. All the three pipes working together can fill the tank in 15 minutes. Thecapacity of the tank is:
A.60 gallons B.100 gallons
C.120 gallons D.180 gallons
Answer: Option C
Explanation:
Work done by the waste pipe in 1 minute =1
-1
+1
15 20 24
=1
-11
15 120
= -1
. [-ve sign means emptying]40
Volume of1
part = 3 gallons.40
Volume of whole = (3 x 40) gallons = 120 gallons.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 28
22.A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B andB is twice as fast as A. How much time will pipe A alone take to fill the tank?A.20 hours B.25 hours
C.35 hours D.Cannot be determined
E.None of these
Answer: Option C
Explanation:
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will takexand
xhours respectively to fill the tank.
2 4
1+
2+
4=
1
x x x 5
7=
1
x 5
x = 35 hrs.
23.Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately,then B would have taken 6 hours more than A to fill the cistern. How much time will be takenby A to fill the cistern separately?
A.1 hour B.2 hours
C.6 hours D.8 hours
Answer: Option C
Explanation:
Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1+ 1 =1
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 29
x (x + 6) 4
x + 6 + x=
1
x(x + 6) 4
x2 - 2x - 24 = 0
(x -6)(x + 4) = 0
x = 6. [neglecting the negative value of x]
24. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes areused together, then how long will it take to fill the tank?
A.12 min B.15 min
C.25 min D.50 min
Answer: Option A
Explanation:
Part filled by A in 1 min =1
.20
Part filled by B in 1 min =1
.30
Part filled by (A + B) in 1 min =1
+1
=1
.20 30 12
Both pipes can fill the tank in 12 minutes.
25.. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both thepipes are opened together but after 4 minutes, pipe A is turned off. What is the totaltime required to fill the tank?
A.10 min. 20 sec. B.11 min. 45 sec.
C.12 min. 30 sec. D.14 min. 40 sec.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 30
Answer: Option D
Explanation:
Part filled in 4 minutes = 41
+1
=7
.15 20 15
Remaining part = 1 -7
=8
.15 15
Part filled by B in 1 minute =1
20
1:
8:: 1 : x
20 15
x =8
x 1 x 20 = 102min = 10 min. 40 sec.
15 3
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
26. One pipe can fill a tank three times as fast as another pipe. If together the two pipes canfill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
A. 81 min. B.108 min.
C. 144 min. D.192 min.
Answer: Option C
Explanation:
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipe will fill it inxminutes.
3
1
+
3
=
1
x x 36
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 31
4=
1
x 36
x = 144 min.
27. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutesrespectively. How many minutes will it take to fill the tanker from empty state if B isused for half the time and A and B fill it together for the other half?
A. 15 min B.20 min
C. 27.5 min D.30 min
Answer: Option D
Explanation:
Part filled by (A + B) in 1 minute =1
+1
=1
.60 40 24
Suppose the tank is filled in x minutes.
Then,x 1
+1
= 12 24 40
xx
1= 1
2 15
x = 30 min.
28. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps areopened. What is the total time taken to fill the tank completely?
A.3 hrs 15 min B.3 hrs 45 min
C.4 hrs D.4 hrs 15 min
Answer: Option B
Explanation:
Time taken by one tap to fill half of the tank = 3 hrs.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 32
Part filled by the four taps in 1 hour = 4 x1
=2.
6 3
Remaining part = 1 -1
=1.
2 2
2:1:: 1 : x
3 2
x =1x 1 x
3=
3hours i.e., 45 mins.
2 2 4
So, total time taken = 3 hrs. 45 mins.
29. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is openall the time and B and C are open for one hour each alternately, the tank will be full in:
A.6 hours B.62hours
3
C.7 hours D.71hours
2
Answer: Option C
Explanation:
(A + B)'s 1 hour's work =1
+1
=9
=3
.12 15 60 20
(A + C)'s hour's work =1
+1
=8
=2
.12 20 60 15
Part filled in 2 hrs =3
+2
=17
.20 15 60
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 33
Part filled in 6 hrs = 3 x17
=17
.60 20
Remaining part = 1 -17
=3
.20 20
Now, it is the turn of A and B and3
part is filled by A and B in 1 hour.20
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
30. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours,C is closed and A and B can fill the remaining part in 7 hours. The number of hours takenby C alone to fill the tank is:
A. 10 B.12
C. 14 D.16
Answer: Option C
Explanation:
Part filled in 2 hours =2=
1
6 3
Remaining part = 1 -1
=2.
3 3
(A + B)'s 7 hour's work =2
3
(A + B)'s 1 hour's work =2
21
C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }
=1-
2=
1
6 21 14
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 34
C alone can fill the tank in 14 hours.
31. If both the pipes are opened, how many hours will be taken to fill the tank?I. The capacity of the tank is 400 litres.
II. The pipe A fills the tank in 4 hours.III. The pipe B fills the tank in 6 hours.
A. Only I and II
B. Only II and III
C. All I, II and III
D. Any two of the three
E. Even with all the three statements, answer cannot be given.
Answer: Option B
Explanation:
II. Part of the tank filled by A in 1 hour =1
4
III. Part of the tank filled by B in 1 hour =1
6
(A + B)'s 1 hour's work =1+
1=
5
4 6 12
A and B will fill the tank in12
hrs = 2 hrs 24 min.5
So, II and III are needed.
Correct answer is (B).
32. How much time will the leak take to empty the full cistern?I. The cistern is normally filled in 9 hours.
II. It takes one hour more than the usual time to fill the cistern because of la leak in thebottom.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 35
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Answer: Option E
Explanation:
I. Time taken to fill the cistern without leak = 9 hours.
Part of cistern filled without leak in 1 hour =1
9
II. Time taken to fill the cistern in presence of leak = 10 hours.
Net filling in 1 hour =1
10
Work done by leak in 1 hour =1-
1=
1
9 10 90
Leak will empty the full cistern in 90 hours.
Clearly, both I and II are necessary to answer the question.
Correct answer is (E).
33.How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B areopened simultaneously?
I. A can fill the tank in 16 minutes.II. B can empty the full tank in 8 minutes.A.I alone sufficient while II alone not sufficient to answerB.II alone sufficient while I alone not sufficient to answerC.Either I or II alone sufficient to answerD.Both I and II are not sufficient to answerE.Both I and II are necessary to answer
Answer: Option E
Explanation:
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 36
I. A's 1 minute's filling work =1
16
II. B's 1 minute's filling work =1
8
(A + B)'s 1 minute's emptying work =1-
1=
1
8 16 16
Tank will be emptied in 16 minutes.
Thus, both I and II are necessary to answer the question.
Correct answer is (E).
34.Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe Bfills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains thetank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed andpipe B is kept open for a minute and then closed and then pipe C is kept open for a minuteand then closed and the cycle repeated, how long will it take for the empty tank to overflow?(1) 42 minutes(2) 14 minutes(3) 39 minutes(4) 40 minutes 33 seconds(5) None of these
Correct Choice - (5). Correct Answer is None of theseExplanatory Answer
Pipe A fills the tank at the rate of 40 litres a minute. Pipe B at the rate of 30 litres a minuteand Pipe C drains the tank at the rate of 20 litres a minute.If each of them is kept open for a minute in the order A-B-C, the tank will have 50 litres ofwater at the end of 3 minutes.After 13 such cycles, the tank will have 13 * 50 = 650 litres of water.It will take 13 * 3 = 39 minutes for the 13 cycles to be over.At the end of the 39th minute, Pipe C will be closed and Pipe A will be opened. It will add 40litres to the tank.Therefore, at the end of the 40th minute, the tank will have 650 + 40 = 690 litres of water.At the end of the 40th minute, Pipe A will be closed and Pipe B will be opened. It will add 30litres of water in a minute.Therefore, at the end of the 41st minute, the tank will have 690 + 30 = 720 litres of water.But then at 700 litres, the tank will overflow. Therefore, Pipe B need not be kept open for afull minute at the end of 40 minutes.Pipe B needs to add 10 more litres of water at the end of 40 minutes. It will take 1/3rd of a
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 37
minute to fill 10 litres of water.Therefore, the total time taken for the tank to overflow = 40 minutes + 1/3 of a minuteor 40 minutes 20 seconds.
35.A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3.The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is theemptying capacity of the pump if the pump needs 12 more minutes to fill the tank than toempty it?
1. 50 m3 / min2. 60 m3 / min3. 45 m3 / min4. 90 m3 /min5. 72 m3 /min
Correct Choice - (2). Correct Answer is 60 m3 / min
Explanatory Answer
Let 'f' m3/min be the filling capacity of the pump.Therefore, the emptying capacity of the pump will be = (f + 10 ) m3 / min.
The time taken to fill the tank will be = minutes
And the time taken to empty the tank will be = .We know that it takes 12 more minutes to fill the tank than to empty it
i.e = 12
=> 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)
=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.
Solving for positive value of 'f' we get, f = 50.
Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 38
36.There are three taps A, B and C in a container. Tap A and B can fill the container in 15and 10 minutes respectively, if they are working alone. Tap C can empty it in 12 minutes ifit is working alone. Initially all the Taps are closed. Tap A is opened alone for 3 minutes.Now A is closed and B is opened alone for 2 minutes. Now B is closed and C is openedalone for 5 minutes. Finally all the three taps are opened together. How long will it take tofill the tank?
10 minutes
12 minutes
Tank Cannot be filled
None of these
Answer :12 minutes
Solution (Fast Approach)
Part 1
Tap A alone can fill 100% of the container in 15 min.Its opened for 3 minutes. Hence it fills (3/15)x100 = 20% of the conatainer
In the same way in 2 minute B can fill (2/10)x100 = 20%.
Now container is 40% full
Now Tap C is opened for 5 min. It can empty (5/12)x100 = 41.67% of the container in 5min. Only 40% of the container is filled, hence C will completely empty the container.Part 2
In 1 min A, B and C combined can fill (1/15 + 1/10 - 1/12) = 1/12 portion of the container
Hence 1 portion (Full) can be filled in 1/(1/12) = 12 minutes
37. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipesare opened simultaneously, how much time will be taken to fill the tank?
Sol. Part filled by A In 1 hour = 1/36Part filled by B in 1 hour = 1/45Part filled by (A + B) In 1 hour = [1/36 + 1/45] = 9/180 = 1/20Hence, both the pipes together will fill the tank in 20 hours.
38. A pipe can fill a tank in 16 hours. Due to a leak in the bottom,it is filled in 24 hours. If thetank is full, how much time will the leak take to empty it ?
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 39
Sol. Work done by the leak in 1 hour = [ 1/16 – 1/24 ]=1/48:. Leak will empty the full cistern in '48 hours.
39. A cistern is filled by pipe A in 10 hours and the full cistern can be leaked out by anexhaust pipe B in 12 hours. If both the pipes are opened, in what time the cistern is full?Sol. Work done by the inlet in 1 hour: = 1/10Work done by the outlet in 1 hour = 1/12Net part filled in 1 hour = [ 1/10 – 1/12 ] = 1/60The cistern will be full in 60 hours.
40. Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are openedsimultaneously and it is found that due to leakage in the bottom, 32 minutes extra are takenfor the cistern to be filled up. When the cistern is full in what time will the leak empty it ?Sol. Work done by .the two pipes in 1 hour = [ 1/14 + 1/16 ] = 15/112... Time taken by these pipes to fill the tank = 112/15 hours
= (7 hrs. 28 min.)Due to leakage, time taken = (7 hrs 28 min.) + 32 min. = 8 hrsWork done by ( two pipes + leak) in 1 hour = 1/8Work done by the leak m 1 hour = [ 15/112 – 1/8 ] = 1/112Leak will empty the full cistern in 112 hours
41. Pipes A and B can fill a tank in 20 hours and 30 hours respectively and pipe C can emptythe full tank in 40 hours. If all the pipes are opened together, how much time will be neededto make the tank full ?
Sol. Net part filled m 1 hour = [1/20 + 1/30 – 1 /40] = 7/120The tank will be full in 120/7 = 17 ½
42. Two pipes A and B can frll a tank in 24 min. and 32 min. respectively. If both the pipesare opened simultaneously, after how much time B should be closed so that the tank is full in18 minutes?
Sol. Let B be closed after x minutes. Then,part filled by (A + B) in x min. + part filled by A in (18 - x) min. = 1.X {1/24 + 1/32] + (18 – x) X 1/24 = 1 or 7x/96 + (18 – x)/24 = 17x + 4(18 –x) = 96 or x=8Hence, B must be closed after 8 minutes
43. Two pipes A and B can fill a tank in 36 min. and 4S min. respectively. A water pipe Ccan empty the tank in 30 min. First A and B are opened. After 7 minutes, C is opened. In howmuch time, the tank Is full ?
Sol. Part filled in 7 min = 7[ 1/36 + 1/45] = 7/20
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 40
Remaining part = [ 1- 7/20] = 13/20
Net part filled in 1 min. When A,B and C are opened
= [ 1/36 + 1/45 + 1/30 ] = 1/60Now, 1/60 part is filled in 1 min.
13/20 part is filled in [60x13/20] = 39 minTotal time taken to fill the tank = (39 + 7) min. = 46 min.
44.There are 12 pipes that are connected to a tank. Some of them are fill pipes and the othersare drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipescan drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, anempty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
(1) 6(2) 8(3) 7(4) 5(5) 4
Correct Choice - (3). Correct Answer is 7 pipes
Explanatory Answer
Let there be 'n' fill pipes attached to the tank.
Therefore, there will be 12 - n drain pipes attached to the tank
Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill th ofthe tank in an hour.
Hence, n fill pipes will fill of the tank in an hour.
Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will
drain th of the tank in an hour.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 41
Hence, (12 - n) drain pipes will drain th of the tank in an hour.
When all these 12 pipes are kept open, it takes 24 hours for an empty tank to
overflow. Therefore, in an hour th of the tank gets filled.
Hence, .
i.e. or 7n - 48 = 1 => 7n = 49 or n = 7.
45. Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept openthroughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes afterpipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equalshare of the tank. Furthermore, it is known that if pipe A and B are kept open continuously,the tank would be filled completely in t minutes. Find t?
A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill theentire tank in '3t' minutes.
A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.A and B together can fill 1/t of the tank in a minute. A alone can fill 1/3t of the tank in aminute. So, in a minute, B can fill 1/t - 1/3t = 2/3t. Or, B takes 3t/2 minutes to fill an entiretank
To fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.
t/2 = t - 10, t = 20 minutes.
A takes 60 mins to fill the entire tank, B takes 30 minutes to fill the entire tank. A is keptopen for all 20 minutes. B is kept open for 10 minutes.
C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tankin 24 minutes.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 42
46.Pipe A fills a tank at the rate of 100lit/min, Pipe B fills at the rate of 25 lit/min, pipe C
drains at the rate of 50 lit/min. The three pipes are kept open for one minute each, one after
the other. If the capacity of the tank is 7000 liters, how long will it take to fill the tank if
i) A is kept open first, followed by B and then C
Each cycle of 3 minutes, 75 liters get filled. 100 + 25 - 50. So, after 3 minutes the tank would
have 75 liters
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
279 mins - 6975 liters
In the 280th minute, pipe A would be open and it would fill the remaining 25 liters in 15
seconds. So, it would take 279 mins and 15 seconds to fill the tank.
The most important thing in these type of questions is to think in terms of cycles till we reach
close to the required target and then think in simple steps.
ii) B first, followed by A, and then C
Each cycle of 3 minutes, 75 liters get filled. 25 + 100 - 50. So, after 3 minutes the tank would
have 75 liters
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
279 mins - 6975 liters
In the 280th minute, pipe B would be open and it would fill the remaining 25 liters in one
minutes. So, it would take 280 mins.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 43
iii) B first, followed by C, and then A
In this case also, Each cycle of 3 minutes, 75 liters get filled. 25 -50 + 100. But there is a
small catch here. In the first set of 3 minutes, we would fill up to about 100 liters. After 1
minute, we would be at 25 liters, after 2 minutes, we would be at 0 liters and in the third
minute, the tank would be 100 liters full.
6 mins - 170 liters
9 mins - 250 liters
30 mins - 775 liters
270 mins - 6775 liters
273 mins - 6850 liters
276 mins - 6925 liters
279 minutes - 7000 liters
So, it would take 279 mins and 15 seconds to fill the tank.
The mOst Important thing in these type of questions is to think in terms of cycles till we
reach close to the required target and then think in simple steps.
47. A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system
of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which
of the following are possible values of n (More than one option could be correct)?
1) 32 2) 54 3) 29 4) 40
3 fill pipes cancel out 2 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5
hours. so the answer has to be 5k + 4. Both 54 and 29 are possible.
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 44
PROBLEMS FOR THE TEST
1.Two taps A and B can fill a tank in 10 hours and 15 hours and 15 hours respectively. Ifboth the taps are opened together, the tank will be full in ?
Ans:6hrs
2.To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The timein minutes that the three pipes together will take to fill the cistern is
Ans:5
3.Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties the fulltank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank willbe filled?
Ans;7 hrs 30 mins
4.A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If thecistern is full, then the time that the leak will take to empty it is
Ans:90 hrs
5.an electric pump can fill a tank in 3 horus. Because of a leak in the tank, it took 3 ½ hoursto fill the tank. The leak can drain out of all the water of the tank in
Ans:21 hrs
6.Taps A and B can fill a bucket in 12 minutes and 15 minutes resp. If both are opened and Ais closed after 3 minutes. How much further time would it take for B to fill the bucket?
Ans 8 min 15 sec
7.A tank can be filled by a tap in 20 minutes and by another rtap in 60 mintues. Both taps arekept open for 10 mintues and then the first tap is shut off. After this, the tank will becompletely filled in
Ans:20 min
8.If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipe fillsthe reservoir 10 hours faster than the other. How many hours it takes the second pipe to fillthe reservoir?
Ans:30 hours
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 45
9.One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. Howlong will they take to fill the cistern if both the taps are opened?
Ans: 6hours
10.12 buckets of water fill a taken when the capacity of each bucked is 13.5 liter. How manybuckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres ?
Ans:18
11.Bucket p has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill theempty drum. How many turns it will take for both the buckets p and q having each turntogether to fill the empty drum
ans:45
12.Two pipes A and B fill a tank in 15 hours and 20 hours respectively while a third pipe ccan empty the full tank in 25 hours. All the three pipes are opened in the beginning, after 10horus, c is closed. In how much time, will the tank be full ?
ans:12 hrs
13.Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respt but a thirdpipe c can empty the full tank in 6 mintues. A and B are kept open for 5 minutes in thebeginning and then c is also opened. In what time is the cistern emptied …..
Ans:45 mints
14.Three pipes A,B and C can fill a tank in 6 hours. After working at it together for 2hours, Cis closed and A and B can fill the remaining part in 7 hours. The number of hours taken by Calone to fill the cistern is
ans:14
15.A leak in the bottom of atank can empty the full tank in 8 hours. An inlet pipe fills waterare the rate of 6 literes a minute. When the tank is full, the inlet is opened and due to the leak,the tank is empty in 12 hours. How many litres does the cistern hold ?
Ans: 8,640
16.A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills waterat the rate of 4 liters a minute. When the tank is full the inlet is opened and due to the leak thetank is empty in 8 hours. The capacity of the tank (in litters is :
Ans 5760.
17.A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank isalready half-full and both tansk are opened together, the tank will be :
Reasoning and Quantitative aptitude Pipes and Cisterns
SITAMS Page 46
ans:emptied in 8 min
18.A cistern has two taps which fill it in 12 min and 15 min resp. There is also a waste pipe inthe cistern. When all the three are opened, the empty cistern is full in 20 minutes. How longwill waste pipe take to empty the full cistern ?
Ans;10 min
19.Two pipes A and B can fill a cistern in 12 minutes and 15 mint resp. If both the pipes areopened together, then after how much time B should be closed so that the tank is full in 9minutes?
Ans 4 min
20.Two pipes A and B can fill a tank in 6 hours and 4 hours resp. If they are opened onalternate hours and if pipe A is opened first, in how many hours, the tank shall be full ?
Ans: 5 hours
21.Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipesare open,in how many hours will the tank be filled ?
Ans:
22.A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fillthe tank. The leak can drain all the water of the tank in
A. 5 hours B. 7 hours
C. 8 hours D. 14 hours
Ans:Leak will empty the tank in 14 hours
23.Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3gallons per minute. All the three pipes working together can fill the tank in 15 minutes. Thecapacity of the tank is
A. 60 gallons B. 80 gallons
C. 120 gallons D. 160 gallons
part filled by (A+B+C) in 1 hour= (1/5 + 1/6 + 1/30)
‹=› 1/3.
All the three pipes together will fill the tank in 3 hours.
Ans:Work done by the waste pipe in 1minute = 1/15 - (1/20+1/24)
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24.Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties thefull tank in 20 hours.If all the three pipes operate simultaneously, in how much time will the tankbe filled?
A. 7 hrs 30 min B. 7 hrs 45 min
C. 8 hrs 30 min D. 8 hrs 45 min
BANK EXAM QUESTIONS
25 A cistern can be filled by pipe A and B in 12 minutes and 10 minutes respectively. Thefull tank can be emptied by a third pipe C in 8 minutes only. If all the taps be turned on at thesame time, the cistern will be full in how much time?
Ans:17(1/7) Minutes
26 Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both the pipesopen together how much time will it take to fill the tank?
Ans:6 Hours
27. Two pipes A and B can fill a tank in 60 minutes. If pipe A alone can fill it in 75 minutes.How much time will the pipe B take to fill the tank alone?
Ans:300 Minutes
28. Three pipes A, B and C can fill a tank in 30 hours, 20 hours and 10 hours respectively. Ifall the pipes open together how much time is required to make the tank full?
Ans:5 (5/11) Hours
= (1/15 - 11/20)
= - 1/40 [ - ve sigh meansemptying]
Volume of 1/40 part = 3 gallons.
Volume of Whole = (3×40)
=120 gallons.
Net apart filled in 1 hour = (1/10+1/12-1/20)
= 8/60
= 2/15.
Therefore the tank will be full in 15/2 hours ‹=› 7 hrs 30 min.
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29. Three pipes A, B and C together can fill a tank in 15 minutes. One of the pipes can fill itin 45 minutes and another in 30 minutes. How much time is taken by the third pipe alone tomake the tank full?
Ans:90 Minutes
30. A cistern can be filled by pipe A and B in 40 minutes and 60 minutes respectively. Thereis also an outlet C. If all the taps are open together the tank is full in 2 hours. How much timeis taken by C to empty the full tank?
Ans:30 Minutes
31. A cistern can be filled by pipe A and B in 30 minutes and 45 minutes respectively. Thereis also an outlet C. If all the taps are open together the tank is full in 1 hour and 15 minutes.How much time is taken by C to empty the full tank?
Ans:23 (13/19) Minutes
32. Pipe A can fill the tank in 12 minutes and pipe B can empty it in 8 minutes. If 3/4th part ofthe tank is already full and both the pipes are open together. In much time both the pipesempty the tank?
Ans:18 Minutes
33.A pipe can fill a tank in 40 minutes. Due to the leakage in the bottom it is filled in 50hours. If the tank is full, how much time will the leak take to empty it?
Ans:200 Minutes
34.P, Q and R are three pipes connected to a tank. P and Q together fill the tank in 4 hours. Rand Q together fill the tank in 6 hours. P and R together fill the tank in 5 hours. In how muchtime will P, Q and R fill the tank together?
Ans:3(9/37) Hours
35. Two pipes A and B can fill a tank in 25 minutes and 35 minutes respectively. But a thirdpipe C can empty it in 10 minutes. The first two pipes are kept open for 5 minutes in thebeginning and then the third pipe is also opened. In what time is the cistern emptied?
Ans:10(10/11) Hours
36. A cistern can be filled by pipe A and B in 25 hours and 30 hours respectively. There isalso an outlet C which can empty it in 40 hours. If all the taps are open together. After 5minutes pipe C must be turned off. In how much time the cistern is full?
Ans:10(15/44) Hours
37. A tank has a leak which would empty it in 16 hours. A tap is turned on which admits 12liter a minute into the tank and it is now emptied in 24 hours. How many liters does the tankhold?
Ans:34560 Liters
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38.Two pipes A and B can fill a tank in 12 minutes and 16 minutes respectively. If both thepipes open together after how much time should be B closed so, that the tank is full in 9minutes?
Ans:4 Hours
39.Two pipes A and B can fill a tank in 10 hours and 12 hours respectively. B is open for 2hours in the beginning, and then B is closed. In how much time A fill the remaining tank?
Ans:8(1/3) Hours
40.Two pipes A and B can fill a tank in 50 minutes and 60 minutes respectively. If both thepipes open together for 10 minutes, then B is closed. In how much time A fill the remainingtank?
Ans:38 Minutes
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25.A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills waterat the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak,the tank is empty in 12 hours. How many litres does the cistern hold ?
A. 7580 B. 7960
C. 8290 D. 8640
Ans:Work done by the inlet in 1 hour
= (1/8 - 1/12)
= 1/24.
Work done by the inlet in 1 min.= (1/24 × 1/60)
= 1/1440.
Volume of 1/1440 part = 6 litres.
Therefore, Volume of whole= (1440×6)
‹=› 8640 litres.